73edo

← 72edo

73edo

74edo →

Prime factorization	73 (prime)
Step size	16.4384¢
Fifth	43\73 (706.849¢)
Semitones (A1:m2)	9:4 (147.9¢ : 65.75¢)
Consistency limit	7
Distinct consistency limit	7

73 equal divisions of the octave (abbreviated 73edo or 73ed2), also called 73-tone equal temperament (73tet) or 73 equal temperament (73et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 73 equal parts of about 16.4 ¢ each. Each step represents a frequency ratio of 2^1/73, or the 73rd root of 2.

Theory

73edo has a very sharp tendency, with the approximations of 3, 5, 7, 11 all sharp. The equal temperament tempers out 78732/78125 and 262144/253125 in the 5-limit; 126/125 and 245/243 in the 7-limit; 176/175, 441/440 and 4000/3993 in the 11-limit; 91/90, 169/168, 196/195, 325/324, 351/350 and 352/351 in the 13-limit. It provides the optimal patent val for the marrakesh temperament, though 104edo and 135edo tunes it better.

73edo fits in mavila scale, by the 9;5 relation in the superdiatonic scheme.

Prime harmonics

Approximation of prime harmonics in 73edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	absolute (¢)	+0.00	+4.89	+8.21	+1.04	+7.59	-2.17	-6.33	-1.62	-3.62	+6.04	+5.65
	relative (%)	+0	+30	+50	+6	+46	-13	-38	-10	-22	+37	+34
Steps (reduced)		73 (0)	116 (43)	170 (24)	205 (59)	253 (34)	270 (51)	298 (6)	310 (18)	330 (38)	355 (63)	362 (70)

Subsets and supersets

73edo is the 21st prime edo, past 71edo and before 79edo.

Intervals

Steps	Cents	Ups and downs notation	Approximate ratios
0	0	D	1/1
1	16.4384	↑D, ↓3E♭	78/77
2	32.8767	↑↑D, ↓↓E♭	49/48, 55/54, 65/64, 66/65
3	49.3151	↑3D, ↓E♭	36/35, 40/39, 65/63
4	65.7534	↑4D, E♭	80/77
5	82.1918	↑5D, ↓8E	21/20, 22/21
6	98.6301	↑6D, ↓7E	35/33, 52/49
7	115.068	↑7D, ↓6E	77/72
8	131.507	↑8D, ↓5E	14/13, 27/25
9	147.945	D♯, ↓4E	12/11
10	164.384	↑D♯, ↓3E	11/10
11	180.822	↑↑D♯, ↓↓E	10/9, 39/35, 49/44, 72/65
12	197.26	↑3D♯, ↓E
13	213.699	E	44/39
14	230.137	↑E, ↓3F	8/7, 63/55
15	246.575	↑↑E, ↓↓F
16	263.014	↑3E, ↓F	7/6, 65/56
17	279.452	F
18	295.89	↑F, ↓3G♭	77/65
19	312.329	↑↑F, ↓↓G♭	6/5
20	328.767	↑3F, ↓G♭	40/33
21	345.205	↑4F, G♭	11/9, 39/32, 49/40
22	361.644	↑5F, ↓8G	16/13
23	378.082	↑6F, ↓7G
24	394.521	↑7F, ↓6G	44/35, 49/39, 63/50
25	410.959	↑8F, ↓5G	14/11, 80/63
26	427.397	F♯, ↓4G	77/60
27	443.836	↑F♯, ↓3G	35/27
28	460.274	↑↑F♯, ↓↓G	64/49, 72/55
29	476.712	↑3F♯, ↓G	21/16, 33/25
30	493.151	G	4/3, 65/49
31	509.589	↑G, ↓3A♭
32	526.027	↑↑G, ↓↓A♭	27/20, 65/48
33	542.466	↑3G, ↓A♭	15/11, 48/35
34	558.904	↑4G, A♭
35	575.342	↑5G, ↓8A	39/28
36	591.781	↑6G, ↓7A
37	608.219	↑7G, ↓6A	77/54
38	624.658	↑8G, ↓5A	56/39, 63/44
39	641.096	G♯, ↓4A
40	657.534	↑G♯, ↓3A	22/15, 35/24
41	673.973	↑↑G♯, ↓↓A	40/27, 65/44, 81/55
42	690.411	↑3G♯, ↓A
43	706.849	A	3/2
44	723.288	↑A, ↓3B♭	32/21, 50/33
45	739.726	↑↑A, ↓↓B♭	49/32, 55/36
46	756.164	↑3A, ↓B♭	54/35, 65/42
47	772.603	↑4A, B♭
48	789.041	↑5A, ↓8B	11/7, 63/40
49	805.479	↑6A, ↓7B	35/22, 78/49
50	821.918	↑7A, ↓6B	77/48
51	838.356	↑8A, ↓5B	13/8, 81/50
52	854.795	A♯, ↓4B	18/11, 64/39, 80/49
53	871.233	↑A♯, ↓3B	33/20
54	887.671	↑↑A♯, ↓↓B	5/3
55	904.11	↑3A♯, ↓B
56	920.548	B
57	936.986	↑B, ↓3C	12/7
58	953.425	↑↑B, ↓↓C
59	969.863	↑3B, ↓C	7/4
60	986.301	C	39/22
61	1002.74	↑C, ↓3D♭
62	1019.18	↑↑C, ↓↓D♭	9/5, 65/36, 70/39
63	1035.62	↑3C, ↓D♭	20/11
64	1052.05	↑4C, D♭	11/6
65	1068.49	↑5C, ↓8D	13/7, 50/27
66	1084.93	↑6C, ↓7D
67	1101.37	↑7C, ↓6D	49/26, 66/35
68	1117.81	↑8C, ↓5D	21/11, 40/21
69	1134.25	C♯, ↓4D	77/40
70	1150.68	↑C♯, ↓3D	35/18, 39/20
71	1167.12	↑↑C♯, ↓↓D	65/33
72	1183.56	↑3C♯, ↓D	77/39
73	1200	D	2/1

Scales

Palace (subset of Porky[15])

• 164.384
• 328.767
• 493.151
• 706.849
• 871.233
• 1035.616
• 1200.000

Music

Claudi Meneghin

• Little Fugue on Happy Birthday